S. Brown, J. Cao, and J. L. Musfeldt University of Tennessee N. Dragoe Universit´e Paris-Sud F. Cimpoesu Institute of Physical Chemistry, Romania R. J. Cross Yale University In Search of Microscopic Evidence of Negative Thermal Expansion in Fullerenes

Negative Thermal Expansion : ZrW 2 O 8 Ernst et al., Nature, 396,147 (1998) Lattice Constant Gruneisen Parameter Thermal volumetric expansion coefficient  ≈  K -1 Lattice expands at low temperature – Bulk effect Sm 2.72 C 60 and Graphite exhibit Negative Thermal Expansion

Recent Prediction on Molecular Level NTE Kwon et al., PRL, 92, (2004)  -1  K -1 Our Goal: Search for microscopic evidence of NTE at molecular level. T (K) a (Å) We know that : Bulk Effect - Normal

Microscopic Picture of Molecular Level Negative Thermal Expansion High PressureLow Temperature Endohedral Larger Ball Softer Vibrational Frequencies Larger Relaxed Ball Modes Soften

Review of Group Theory Ten Raman active modes 2 A g + 8 H g Four infrared active modes 4 T 1u Point group I h T 1u (1) 527 cm -1 A 1g (1) 100 A 1g (2) 100 T 1u (1) T 1u (2) % Radial % Tangential Our Focus Normal Coordinate Analysis [1] 1 Stanton & Newton, J. Phys. Chem., 92, 2141 (1988) [2] fcc lattice 2

Endohedral Fullerene Inert atoms or molecules inside fullerene cage Cage size effects due to guest host interaction Synthesis : High pressure, Temperature Condition Separation: High-Performance Liquid Chromatography

Our Experiments  C 60 and 60 in polyethylene matrix Suitable for FIR Transmittance measurements  BRUKER IFS 113V Frequency range 20 – 700 cm -1 Temperature range K Resolution – 0.1 cm -1

Infrared Spectra of C 60 and 60 C 60 T 1u (1) Mode Low Temperature Unusual Mode Softening by 0.5 cm -1 60

Temperature Dependent Behavior MP2 level calculation optimizes the cage of 60 as contracted ball C Å Å Cage Radius R ∆R 60 -C 60 ≈ - 1  Å ∆  60 -C 60 ≈ 2 cm -1

Kr Extended X-Ray Absorption Fine Structure (EXAFS) Data on 60 Ito et al., J. Phys. Chem. B, 108, 3191 (2004) Cage Radius Å 300 K Å 77 K Ball is Low Temperature Thermal Expansion Coefficient  ≈ K -1

Microscopic vs. Macroscopic Behavior Low temperature behavior Cage expands - Molecular effect Lattice contracts - Bulk effect Loosdrecht et al., PRL (1992) Hamanaka et al., J. Phys.: Condens. Matter (1995) Lattice Parameter Infrared Raman EXAFS Temperature (K)

Pressure Dependence of Vibrational Spectra Vibrational modes soften with increasing P below 0.4 GPa Snoke et al.,PRB (1992) Meletov et al., Phys. Stat. Sol. (b) (1996)  /  P < 0 H g (3), H g (4), T 1u (1) Consisted with “relaxed ball” Lattice is compressed as P increases   /  P ≈ - 12 Lattice Parameter

Volumetric Expansion Coefficient Thermal expansion will be positive or negative depending upon Grüneisen Parameter  i Mode Grüneisen Parameter Isothermal Compressibility

Mode Grüneisen Parameter (0-0.4 GPa) for C 60 NegativeGrüneisen Parameters Many

Mode Specific Heat Calculation Gompf et al., J. Superconductivity (1994 ) Thermal Expansion Coefficient Specific Heat - No. of phonon /branch of frequency Total No. of Intramolecular Vibrational Modes 46 Raman and Infrared Active Mode 14 Area under the DOS plot

Microscopic Picture Endohedral High PressureLow Temperature Harder, Smaller Ball Higher Vibrational Frequency Due to change in potential and weak guest-host interaction Larger Ball Softer Vibrational Frequencies Larger Relaxed Ball Modes Soften

What We Learned  Measured variable temperature infrared spectra of C 60 and 60  T 1u (1) mode softens throughout the temperature range under investigation  Previous variable temperature Raman and EXAFS, variable pressure Raman consistent  Consistent with predictions for Molecular Negative Thermal Expansion Acknowledgments Division of Materials Research, NSF